The Galois action and cohomology of a relative homology group of Fermat curves

@article{Davis2018TheGA,
  title={The Galois action and cohomology of a relative homology group of Fermat curves},
  author={Rachel Davis and Rachel J. Pries and Vesna Stojanoska and Kirsten Wickelgren},
  journal={Journal of Algebra},
  year={2018}
}
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5 Citations
Background Citations
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5 Citations

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References

SHOWING 1-10 OF 31 REFERENCES
Galois module structure and Jacobians of Fermat curves
The class‐invariant homomorphism allows one to measure the Galois module structure of extensions obtained by dividing points on abelian varieties. In this paper, we consider the case when the abelian…
Galois Action on the Homology of Fermat Curves
In his paper titled “Torsion points on Fermat Jacobians, roots of circular units and relative singular homology,” Anderson determines the homology of the degree n Fermat curve as a Galois module for…
A non-abelian conjecture of Birch and Swinnerton-Dyer type for hyperbolic curves
We state a conjectural criterion for identifying global integral points on a hyperbolic curve over $\mathbb{Z}$ in terms of Selmer schemes inside non-abelian cohomology functors with coefficients in…
Profinite braid groups, Galois representations and complex multiplications
In this paper, we consider two closely correlated subjects. One is a pro-i analogue of the braid group, and the other is a construction of the universal 1-adic power series for complex…
Crystalline Cohomology, Dieudonné Modules, and Jacobi Sums
Hasse [20] and Hasse-Davenport [21] were the first to realize the connection between exponential sums over finite fields and the theory of zeta and L-functions of algebraic varieties over finite…
A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula
We prove a trace formula in stable motivic homotopy theory over a general base scheme, equating the trace of an endomorphism of a smooth proper scheme with the "Euler characteristic integral" of a…
The motivic fundamental group of P1∖{0,1,∞} and the theorem of Siegel
In this paper, we establish a link between the structure theory of the pro-unipotent motivic fundamental group of the projective line minus three points and Diophantine geometry. In particular, we…
Noncommutative cohomologies and Mumford groups
In this note we prove the “quadratic property” of the boundary mapping in the exact sequence of cohomologies. We present calculations for the action of the Galois group on the Mumford group.
Rational Points and Arithmetic of Fundamental Groups: Evidence for the Section Conjecture
Part I Foundations of Sections.- 1 Continuous Non-abelian H1 with Profinite Coefficients.-2 The Fundamental Groupoid.- 3 Basic Geometric Operations in Terms of Sections.- 4 The Space of Sections as a…
A classical introduction to modern number theory
TLDR
This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curve.
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